From my understanding of limit points and interior points there is somewhat of an overlap and that a lot of the time interior points are also limit points.
For the reals, a neighborhood, $r>0$, around a point must contain only a single point of the set in question to determine if it's a limit point or not. However, an interior must be completely contained in the set in question, meaning it has a neighborhood that contains at least a point in the set, which also makes it a limit point.
For example: $[0,1)$ in the reals.
From what I understand the set $(0,1)$ in the set of interior points, the set $[0,1]$ in the set of all limit points, and the set $(0,1)$ is the set of all point which are both interior and limit points.
Is this correct or are interior points always not limit points for some reason?